Summary

Fixes #1174.

This makes the Riccati symmetry checks more robust and avoids false QN must be a symmetric matrix errors when lqe() / dlqe() form the projected process covariance G @ QN @ G.T.

Details

• Replace the local floating-point symmetry check with SciPy's issymmetric / ishermitian using a small scale-aware tolerance.
• Validate user-supplied QN as a symmetric covariance matrix before projection.
• Symmetrize only the projected covariance G @ QN @ G.T, which is mathematically symmetric but can pick up roundoff-level asymmetry.
• Add deterministic regressions for both lqe(..., method="scipy") and dlqe(..., method="scipy").
• Add a guard test showing clearly asymmetric user QN is still rejected instead of silently repaired.

Local validation

• Red proof: using the regression matrices without the projected-covariance symmetrization makes care() and dare() reject G @ QN @ G.T with ControlArgument: QN must be a symmetric matrix; the measured projected asymmetry was 4.44e-16.
• python -m pytest -p no:cacheprovider control\tests\mateqn_test.py::TestMatrixEquations::test_symmetric_shape_check_tolerance -q
• python -m pytest -p no:cacheprovider control\tests\stochsys_test.py::test_lqe_symmetrizes_projected_process_covariance control\tests\stochsys_test.py::test_dlqe_symmetrizes_projected_process_covariance control\tests\stochsys_test.py::test_lqe_rejects_user_supplied_asymmetric_covariance -q
• python -m pytest -p no:cacheprovider control\tests\mateqn_test.py -q -> 11 passed, 13 skipped (slycot not installed)
• python -m pytest -p no:cacheprovider control\tests\stochsys_test.py -q -> 29 passed, 2 skipped (slycot not installed)
• python -m ruff check --no-cache control\mateqn.py control\stochsys.py control\tests\mateqn_test.py control\tests\stochsys_test.py
• PYTHONPYCACHEPREFIX=C:\tmp\pycache-python-control-1174 python -m compileall -q control\mateqn.py control\stochsys.py control\tests\mateqn_test.py control\tests\stochsys_test.py
• git diff --cached --check

AI-assisted contribution disclosure: implementation prepared with OpenAI Codex and reviewed/tested locally before submission.